Question

if q^2-1 is divisible by 8 if q is _____

Answer 1

Answer:

if q is odd

Step-by-step explanation:

Hello,

Either q is odd or is even.

Case 1 - we can find k integer so that q = 2k

Then, in the case

$q^2-1=4k^2-1$

This is not divisible by 8, for instance, q = 6

$q^2-1=36-1=35=7*5$

Case 2 - we can find k integer so that q = 2k+1

$q^2-1=(2k+1)^2-1=4k^2+4k+1-1=4k(k+1)$

k(k+1) is divisible by 2 so the initial number is divisible by 8

Conclusion, the answer is q is odd.

Thanks